A multi-objective stochastic optimization approach for estimation of subsurface geomodels

Abstract

We present a multi-objective optimization approach to the subsurface geomodel updating problem using stochastic search techniques. This is a new approach to the geomodeling process for which a variety of direct and indirect measurements can be simultaneously fit to the geomeodel. Due to the inherent uncertainties and noise in real data measurements, geological and geophysical datasets acquired in the same area may be in conflict with each other; and a realistic subsurface model can only be obtained by simultaneously integrating the combined datasets in a reasonable manner. One approach to this problem is to perform joint inversion of multiple geological and/or geophysical datasets, where an optimal model is achieved by optimization of a linear combination of several objective functions measuring the match of the simulated datasets with the observed datasets. In this paper, we consider joint inversion of multiple datasets for geomodel updating, as a Multi-Objective Optimization Problem (MOOP), where separate objective functions for each subset of the observed data are defined. Then, a stochastic optimization technique is employed to find the set of best-compromise model solutions that fit the defined objectives, which are found along the Pareto front (a set of non-dominated optimal solutions). We demonstrate that a customized initialization of the algorithm can speed up the convergence and result in a set of improved model solutions. An application of the methodology is presented using the example of a 3D reservoir litho-facies model that must honour a set of geological and geophysical attributes (e.g. log data and inverted seismic P- and S-wave impedances). Also, the sensitivity of the model inversion results to changes in the optimization parameters and the presence of seismic noise is analysed.